Problem: Solve for $q$, $ -\dfrac{5q + 5}{25q + 20} = \dfrac{10}{5q + 4} - \dfrac{9}{5q + 4} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $25q + 20$ $5q + 4$ and $5q + 4$ The common denominator is $25q + 20$ The denominator of the first term is already $25q + 20$ , so we don't need to change it. To get $25q + 20$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{10}{5q + 4} \times \dfrac{5}{5} = \dfrac{50}{25q + 20} $ To get $25q + 20$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{9}{5q + 4} \times \dfrac{5}{5} = -\dfrac{45}{25q + 20} $ This give us: $ -\dfrac{5q + 5}{25q + 20} = \dfrac{50}{25q + 20} - \dfrac{45}{25q + 20} $ If we multiply both sides of the equation by $25q + 20$ , we get: $ -5q - 5 = 50 - 45$ $ -5q - 5 = 5$ $ -5q = 10 $ $ q = -2$